Applicability of the two-particle quantization condition to partially-quenched theories

Understand

Partial quenching allows one to consider correlation functions and amplitudes that do not arise in the corresponding unquenched theory.

• For example, physical $s$-wave pion scattering can be decomposed into $I=0$ and $2$ amplitudes, while, in a partially-quenched extension, the larger symmetry group implies that there are more than two independent scattering amplitudes.
• It has been proposed that the finite-volume quantization condition of L\"uscher holds for the correlation functions associated with each of the two-particle amplitudes that arise in partially-quenched theories.
• Using partially-quenched chiral perturbation theory, we show that this proposal fails for those correlation functions for which the corresponding one-loop amplitudes do not satisfy $s$-wave unitarity.